Total Posts:7|Showing Posts:1-7
Jump to topic:

Creating Games: Balancing by Points

Buddamoose
Posts: 19,450
Add as Friend
Challenge to a Debate
Send a Message
10/1/2012 6:16:33 PM
Posted: 4 years ago
Again from the same site, this is an excellent article on a balancing system for mafia games:

Mafia Pointing Theory
By Axelrod

For anyone who has ever attempted to design a Mafia game, one of the most important questions, perhaps the single most important question, that they must ask themselves is this: Is this set-up balanced?

"Balanced" in this context meaning simply, "is this a set-up where both sides have a reasonable chance of winning?" Which is not the same thing as an "equal" chance. Given the host of intangibles present in any Mafia game, creating a set-up in which both sides might be said to have perfectly equal chances of winning is an impossibility. Ideally, one should simply try to create a set-up in which the chances for either side are close enough so that no one will look back at the end and have the extremely frustrating feeling that they never truly had a chance to begin with.

What follows are some of my ideas concerning balance in Mafia games, including the system that I currently use to evaluate games that I review. These are ideas that I developed over a long period of time, based on games played, read, and designed, but which I had never put down into numbers.

In particular, my goal was to see whether or not a "point" based system " one in which all the roles of the game are given a numerical value " could be made to work.*

Obviously no point based system is going to be perfect, but it seemed like a good place to start, and after using this system for more than a year-and-a-half and applying it to many, many different types of Mafia set-ups, I have developed great faith in it.

The Basic Role Values:

Vanilla Townie = 1
Cop = 4
Doc = 3
Vigilante = 3
Role-blocker = 2

Vanilla Mafia = 4.5 (I have tried this several different ways. Valuing a mafia at 5 seems too high, but valuing one at 4 seems slightly low. I therefore, brilliantly, put it right in the middle. How scientific of me)

Where did I get these numbers from? I started by plugging them into some very basic Mafia set-ups (using 25% Mafia as baseline):

12 players: 9 town, 3 mafia

Town = 1
Mafia = 4.5

In this set-up, the town has 9 points (nine vanilla townies worth 1 point each.) The mafia has 13.5 points (three mafia worth 4.5 each.) Because the mafia "score" is higher, the mafia should win a majority of the games using this set-up if it's correct, and I do believe it is correct. To "balance," change 2 of the basic townies to a Cop and Doc. Now the points are: Town 14, Mafia 13.5, which is at least close to being even.

The margin of error I decided on is +/- 1 mafia member (or 4.5 points). In other words, if the points add up so that the two sides are within 4.5 of each other, it shouldn"t play as too unbalanced. The vanilla set-up above is actually within this margin of error, and I believe you could play the vanilla set-up and no one would jump up and down at the end about how unfair it was. Similarly, adding a Vigilante role to the town in addition to the Cop and Doc. doesn"t unbalance the game, it just shifts the odds around a little.

The point isn"t to be exact, but to get things in the ballpark.

20 players: 15 town, 5 mafia

Town = 1
Mafia = 4.5

Here the town has 15 points, while the mafia has 22.5. Again, if you played this exact set-up, I believe the mafia would win a significant majority of the time. If we add a Cop and a Doc. role then the town has 20 points to the mafia"s 22.5. This is much closer, though I think such a set-up still favors the mafia a bit. So again, it seems right.

It is my belief that, for a 20 player game with no abilities (i.e. Mountainous Mafia), the closest balance you can achieve is to have 16 town players (16 points) and 4 mafia players (18 points).

24 players: 18 town, 6 mafia

Town = 1
Mafia = 4.5

Here the town has 18 points, while the mafia has 27. This would appear to swing very strongly in favor of the mafia, and, again, I believe that actual games played would bear out that assumption. You can cut an entire mafia here (I think 5 mafia is probably correct in a 24 player game). At a minimum, you could add a Cop and a Doc., making the town score 23 and Mafia score 27. This is still favoring mafia, which I think is true, but it is definitely closer. Again, whether one agrees on the exact number values doesn"t matter.

The Serial Killer

A Serial Killer (SK) in the mix throws the numbers off. A SK will typically give an edge to the mafia simply by virtue of the fact that he will usually be hitting a townie at least 2/3 more often. How much of an edge the presence of a SK gives is an open question (possibly deserving of it"s own article), but my working premise is that a SK should be valued as an extra mafia - using my numbers = 4.5 points. These would be points added to the total mafia score for purposes of determining game balance.

*Note: I make no effort to balance the SK role itself. His chances of winning are never good, and it would be a great mistake, in my opinion, for a game moderator to try and design a game where the serial killer"s chances were equal to the town and mafia"s.

Returning to a typical 20 player set-up, with a SK in the mix there are two primary ways to distribute the roles. One could have 15 town, 4 mafia, and 1 SK, or 14 town, 5 mafia and 1 SK.

In the former scenario, before counting the SK, the town has 15 points, and the mafia has 18. In the second scenario, the town has 14 points and the mafia score is 22.5.

Counting the SK as an "extra" mafia, then in Scenario #1, the mafia score would go up to 22.5. In the second scenario, the mafia score would go all the way up to 27.

So to "balance" these scenarios for the town, they need more. A Cop/Doc/Vig. gives the town in the first scenario 22 points vs. the mafia 22.5. That"s close. In scenario #2, the Cop/Doc/Vig. gives the town 21 points to the mafia"s 27. This is still not "balanced." Here you would want to give even more power to the town (or simply cut a mafia and go with scenario #1).

All this is with a completely vanilla mafia. If you want to give the mafia any abilities, which most moderators do, then that would increase the value of the mafia roles (over and above the 4.5 they are worth to begin with).

Rough estimates on other Role values:

Back-Up Cop/Doc: 2.5/2
Watcher: 2
Tracker: 2
1-Shot Vigilante: 2
Masons (with confirmation that co-masons are town):
-2 man group: 2 points each, total 4.
-3 man group: 2.5 points each, total 7.5
-4 man group: 3 points each, total 12
(this assumes a large 20+ person game. A Mason group in a mini-game is even more powerful because they make up a larger percentage of the total town. I don't think confirmed Masons should ever represent more than .20% of the total town bodies.)

In addition, it is possible to have roles with negative values which take points away from their respective sides (or are simply worth less than 1). For example, I typically value a "Miller" role on the side of the town as .5 points. He still has some value to the town " he can vote, and provide analysis - but his drawback makes him worth less than even a vanilla townie.

A role that the mafia does not have to eliminate to win (such as a Survivor role) would be zero points, generally speaking.

There are other considerations as well, such as Day Start vs. Night vs. Kill vs. No-kill 1st Night. These I have not examined quite as closely, but I have a few additional premises:

-A day start generally favors the town = +1 to total town score
-Cop Head Start (Night start with use of all abilities but no kills allowed = +2 to town (and this could potentially be even more if the town had multiple investigate roles or more useful actions to take during the night.)
"Reality is an illusion created due to a lack of alcohol"
-Airmax1227

"You were the moon all this time, and he was always there to make you shine."

"Was he the sun?"

"No honey, he was the darkness"

-Kazekirion
F-16_Fighting_Falcon
Posts: 18,324
Add as Friend
Challenge to a Debate
Send a Message
10/1/2012 6:27:59 PM
Posted: 4 years ago
Another awesome article. The one thing I want to add though is that it is a good idea to make the serial killer on par with the town and the mafia as far as chances of winning goes and not merely as a distraction. Why include a serial killer and fvck up your game balance if he doesn't have a chance of winning anyways?
Buddamoose
Posts: 19,450
Add as Friend
Challenge to a Debate
Send a Message
10/1/2012 6:34:55 PM
Posted: 4 years ago
At 10/1/2012 6:27:59 PM, F-16_Fighting_Falcon wrote:
Another awesome article. The one thing I want to add though is that it is a good idea to make the serial killer on par with the town and the mafia as far as chances of winning goes and not merely as a distraction. Why include a serial killer and fvck up your game balance if he doesn't have a chance of winning anyways?

This is definitely a valid question. The way I look at it is, if you include an SK, the best way to balance this is to not include a vigilante. This way the SK has a safe fake-claim, and thus will have a better chance of winning.

Over time I've realized that SK's, and most TP's end up imbalancing a game more so than balancing it. So I'm more so partial to excluding them now than I used to be. Obviously I will still use them, but less often than I would have in the past
"Reality is an illusion created due to a lack of alcohol"
-Airmax1227

"You were the moon all this time, and he was always there to make you shine."

"Was he the sun?"

"No honey, he was the darkness"

-Kazekirion
F-16_Fighting_Falcon
Posts: 18,324
Add as Friend
Challenge to a Debate
Send a Message
10/1/2012 6:39:11 PM
Posted: 4 years ago
That is good idea. However, it severely limits his kill choices to what he can explain in the day thread. I much more like the idea of including a vig specifically so the SK can't claim it and making the SK one of Investigation Innocent/Ninja/Bulletproof or any two but not all three. This way, the kills are "rogue." He could start killing confirmed townies to lower the pool of the confirmeds and increasing the likelihood of a mislynch.

An SK fake-claiming vig wouldn't last, he would have to kill mafia/scummy townies and at some point, through process of elimination, town will catch him if the mafia haven't already killed him.
Logic_on_rails
Posts: 2,445
Add as Friend
Challenge to a Debate
Send a Message
10/2/2012 1:55:17 AM
Posted: 4 years ago
An interesting guide that I would suggest a first time mod might do well to read.

All that said, there's no way I'd ever use this guide! My balancing of games involves creating new roles, variations on existing roles etc. that make a point system unworkable. Furthermore, there's the degree to which information (or misinformation in rare cases) circulates through my OPs, whether I give Mafia additional help etc. Death in Mystere may just have been workable by a point system (if you could determine the value of an inquisitor and head inspector set-up) , but no other game could have been balanced in such a manner.

So, nice concept, but I'd keep this for simple games or beginner games, or mods who frequently overpower one side...
"Tis not in mortals to command success
But we"ll do more, Sempronius, we"ll deserve it
Buddamoose
Posts: 19,450
Add as Friend
Challenge to a Debate
Send a Message
10/2/2012 3:57:41 PM
Posted: 4 years ago
At 10/2/2012 1:55:17 AM, Logic_on_rails wrote:
An interesting guide that I would suggest a first time mod might do well to read.

All that said, there's no way I'd ever use this guide! My balancing of games involves creating new roles, variations on existing roles etc. that make a point system unworkable. Furthermore, there's the degree to which information (or misinformation in rare cases) circulates through my OPs, whether I give Mafia additional help etc. Death in Mystere may just have been workable by a point system (if you could determine the value of an inquisitor and head inspector set-up) , but no other game could have been balanced in such a manner.

So, nice concept, but I'd keep this for simple games or beginner games, or mods who frequently overpower one side...

I wouldnt imagine it would be too difficult to base points off of new roles(they are similar to roles that already exist after all) as well as (mis)information via OP's.
"Reality is an illusion created due to a lack of alcohol"
-Airmax1227

"You were the moon all this time, and he was always there to make you shine."

"Was he the sun?"

"No honey, he was the darkness"

-Kazekirion
Logic_on_rails
Posts: 2,445
Add as Friend
Challenge to a Debate
Send a Message
10/2/2012 4:26:04 PM
Posted: 4 years ago
At 10/2/2012 3:57:41 PM, Buddamoose wrote:

I wouldnt imagine it would be too difficult to base points off of new roles(they are similar to roles that already exist after all) as well as (mis)information via OP's.

Well, I suppose we can agree to disagree. I agree that it's possible, but it's not something I'd be attempting. When making a game you have to make an inherent judgement about balance. To decide on a point value you have to make a judgement, although you somewhat ignore that role's interaction with other roles - cop roles vary in power depending upon the existence of other roles.

For instance, I once had a deputy tracker ... and no tracker. The deputy (based on your chart and it's trends ) would be slightly more valuable than a vanilla. However, the false information given and the expectations the town gets actually serve to perpetuate overconfidence ... it's slightly worse than a vanilla.

Also, not all roles are similar to existing roles, at least not in too noticeable a regard.

Many games can be balanced, and this system has merit. However, for a certain levels of intricacy this guide is a little bit redundant or useless. Most people should consider it though.
"Tis not in mortals to command success
But we"ll do more, Sempronius, we"ll deserve it